FINDING THE SLOPE FROM

2 POINTSDay 91

Learning Target:Students can find the slope of a line from 2 given points.

Linear equations have constant slope (or constant rate of change). For a line on the coordinate plane, slope is the following ratio:

vertical change horizontal change

change in y change in x

=

This ratio is often referred to as , or “rise

over run,” where rise indicates the number of units moved up or down and run indicates the number of units moved to the left or right. Slope can be positive, negative, zero, or undefined. A line with positive slope goes up from left to right. A line with negative slope goes down from left to right.

rise run

Zero Slope

Undefined Slope

Positive Slope

Negative Slope

If you know any two points on a line, you can find the slope of the line without graphing. The slope of a line through the points (x1, y1) and (x2, y2) is as follows:

y2 – y1 x2 – x1

Slope from 2 points Steps:

LABEL, WRITE, PLUG AND CHUG!!

1. Label points

2. Write the slope formula

3. Plug the numbers in the formula

4. Chug out the answers

Find the slope of the line that passes through (–2, –3) and (4, 6).

Let (x1, y1) be (–2, –3) and (x2, y2) be (4, 6).

6 – (–3)4 – (–2)

Substitute 6 for y2, –3 for y1, 4 for x2, and –2 for x1.

96=

The slope of the line that passes through (–

2, –3) and (4, 6) is . 32

=y2 – y1

x2 – x1

32=

Find the slope of the line that passes through (–4, –6) and (2, -3).

Let (x1, y1) be (–4, –6) and (x2, y2) be (2, 3).

3 – (–6)2 – (–4)

Substitute 3 for y2, –6 for y1, 2 for x2, and –4 for x1.

96=

The slope of the line that passes through (–

4, –6) and (2, 3) is . 32

=y2 – y1

x2 – x1

32=

Nonlinear equations have variable rates of change. This means that the rate of change is different between values. This is shown in a graph by a curved line.

(LINEAR)

(NONLINEAR)

(NONLINEAR)

(NONLINEAR)

(NONLINEAR)

(LINEAR)

Find the slope of the line passing through each pair of points.

1. (4, 3) and (–1, 1)

2. (–1, 5) and (4, 2)

25

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Ticket Out The Door

• Draw and label the different types of slope

• What is the slope formula?

• Find the slope from the points (1,7) and (11,12)